Transformer
The picture proofs that the device is an everyday's iron core mains transformer. Leave it like it is, connect the black two wires to mains and measure the output voltages. There should be two voltage outputs, one with a center tap.
To find out which wire belongs to which winding measure the resistance between wires. The winding with the center tap should have the double resistance from outer to outer tap.
You can also find out which wire belongs to one winding by looking sharp where they come from.